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The bridging tractions developed behind a crack tip are considered for a stationary crack under cyclic loading conditions at elevated temperatures in high-toughness, monolithic ceramics. Assuming a temperature range where the grain-boundary phases are sufficiently soft such that bridging can occur due to a viscous layer in the boundary, a viscoelastic model is developed in which bridging forces associated with the shear resistance of the grain-boundary phase are transmitted across the surfaces of a crack. Throughout the work, cyclic and static damage mechanisms which may be operating ahead of the crack tip (e.g. creep cavitation) are ignored in order to focus exclusively on the role of viscous grain bridging. A primary goal is to incorporate microstructural details like grain shape, grain-boundary thickness, and glass viscosity, as well as the effects of external variables such as loading rate and temperature. A fully self-consistent numerical approach is adopted, which does not require any prescribed assumptions as to the shape of the crack-opening profile. The self-consistent solution is compared to an analytical solution for a simplified parabolic approximation of the crack-flank opening displacements. The model is applicable to a wide range of ceramic materials at elevated temperatures, and rationalizes the frequency and temperature sensitivity not generally observed in ceramics at room temperature. Solutions identify a non-dimensional group associated with microstructure and external loading conditions, and solutions are presented over a range of this parameter. |
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